Math 90 - Final Exam Review Sheet
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.
3
2
1
1. Solve the formula - = - - ~ for z
x y z
2. Solve: 'j3x - 71= 5
3. Solve and graph: 12x- 11< 11
4. Solve: X3- 25x= 0
.
7x+2
5. . Find the values where x 3 +2x 2 -15x is undefined.
o .
24 . x2 - 9x + 18
6 . D IVId e.. x2 -1Ox+
2
2x 2 -5x-12 -:- 4x-9
3n
4m3
7. Simplify:
9n
8m
8. Divide using the method of your choice: (x3 - 7x - 6) + (x + 2)
x
6
9. Solve: --3=x-6
x-6
b
2
3
2
10.Solve: ---=
b - 5 b - 6 b - 11b + 30
11. A boat goes 20 miles upstream in the same time it takes to go 60 miles
downstream. The current flows at 4 mph. Find the boat speed (with no
current).
12. Simplify and express in standard form: 3 + ~i
4-1
13. Solve: (3x - 4)2 = 32
14. Solve: -11x2+ 4x - 2 = 0
15. Solve: 2.JP= P- 3
16. Solye and graph: 1- 4y - 21 < 0
17. To get from Roller King (Modesto) to Turlock, I can take Briggsmore 9.6
miles east to Albers/Geer Rd., then go 11.0 more miles south to Turlock.
Assuming that Highway 99 is a perfect diagonal, how many miles is the
diagonal shortcut on Highway 99 between Roller King and Turlock?
18. Graph the equation: y = -3x + 6
19. A case of 24 sodas costs $4, and each soda is sold for $0.50. If the profit is
described by the equation P(x) = 0.5x - 4, where x is the number of sodas
sold,
a) FindP(20)
.
b) What is the break-even point?
20. Graph the linear inequality 2x - 5y .s - 10.
21. Find the slope of the line between the points (-3, 4) and (0,-1).
22. Find the distance between the points (-3, 4) and (0, -1).
23. If a symmetrical roof has a 35% pitch, and the horizontal beam spanning the
base of the entire roof is 60 ft. long, how long is the vertical beam connecting
the base and the peak of the roof?
24. Find the equation of the line with m = ~ which contains the point (4, -6).
25. Find the vertex of and grapl:1the function: f(x) = x? + 6x + 8
-1,...X<-2
26. Graph the function f(x) = 1,...- 2 ~ x < 0
{ x,...x~O
27. Find the domain and range of f(x) = .J9- x
28. Graph: f(x) = 1-x - 31
.
29. Graph: f(x) = %(x + 1)3+ 2
30. For f(x) = x? + 3x - 1 and g(x) = 2x - 5, find (f 0g)(x) and (g 0f)(x)
31. If P varies directly as t and inversely as w, and if p = 27 when t = 18 and w
= 6, find the value of p when t = 8 and w = 3.
32. Solve (1/27)3X= 32x-1
33. Graph: f(x) = - 3-x
34. Find the inverse of f(x) = -3x - 6
35. The half-life of radium is about 1600 years. If the original amount of radium
is 500 grams, how much will remain after 800 years?
36. Solve: 10gsX= -2/3
37. Express as the sum or difference of simpler logarithms with no exponents:
x3.JZ
logs(-s-)
y
38. Solve: log3x+ log3(x - 2) = 1
39. Solve: 22x+ 1 = 3x+1
40. For the following word problem, write a system of equations. Represent this
system as an augmented matrix, but DO NOT SOLVE!
"A trail mix is made from peanuts ($2I1b),raisins ($2.50/lb), and M & M's
($4/lb). A mixture of 22 Ib is made, which costs $55 all together. If the weight
of peanuts is twice the weight of raisins, how much of each type is used?"
41. A system has been reduced so that its augmented matrix is:
1 -3
4
I -4
I3 ]
o 1 -2
[o
42. Find
I
1
I
0
1
5
-3
1
0 1
-1 4
2
2
Solve for x, y, and z.
I
43. Find the vertex and focus of the parabola x? = - 8y
44. Find the equation of the circle with center at (2, -3) and radius = 5. Write
your answerin generalform.
.
45. Find the equation of the ellipse with vertices at (0, 6) & (0, -6), and foci at
(0, J27 ) & (0, - .J27 )
46. Find the vertices and foci, and sketch the hyperbola: 91
47. Solve the system:
-
4x? - 36 = 0
I
y=~-3
,
2x + y == - 4
..
48. Find the sum of the first 50 terms of the sequence 2,6,10,14......
49. Find the general term of the sequence .2, .02, .002, .0002....
50. Find the sum of the first 10 terms of the geometric sequence 5,10,20,40...
51. A pile of logs has 30 logs in the bottom layer, 29 in the next layer, 28 in the
3rdlayer, with one less in each successive layer, and 1 log in the top layer.
How many logs are in the pile?
52. Change the repeating decimal .321 to a fraction.
53. Findthe sumof the infinitegeometricsequence,Is.
(..!.)i
2
54. How many committees of 2 Republicans and 2 Democrats can be chosen
from a group of 5 Republicans and 7 Democrats?
55. How many leadership teams of a president, a vice-president, and a
secretary can be selected from 10 people?
56. Expand the binomial (a + 2b)6
i=1
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